Let's consider the salaries of Amrita and Sarita to answer the question on the percentage by which Sarita's salary is less than Amrita's salary.
Let Sarita's salary be [tex]\( S \)[/tex]. According to the problem, Amrita's salary is [tex]\( 20\% \)[/tex] more than Sarita's salary.
Step 1: Expressing Amrita's salary in terms of Sarita's salary.
[tex]\[ \text{Amrita's Salary} = S + 0.20 \times S = 1.20 \times S \][/tex]
Step 2: Calculate the difference in their salaries.
[tex]\[ \text{Difference} = 1.20 \times S - S = 0.20 \times S \][/tex]
Step 3: Calculate the percentage difference based on Amrita's salary.
[tex]\[
\text{Percentage by which Sarita's salary is less} = \left( \frac{\text{Difference}}{\text{Amrita's Salary}} \right) \times 100
\][/tex]
[tex]\[
= \left( \frac{0.20 \times S}{1.20 \times S} \right) \times 100
\][/tex]
[tex]\[
= \left( \frac{0.20}{1.20} \right) \times 100
\][/tex]
[tex]\[
= \frac{20}{120} \times 100
\][/tex]
[tex]\[
= \frac{1}{6} \times 100
\][/tex]
[tex]\[
= 16.666666666666664\%
\][/tex]
So, Sarita's salary is approximately [tex]\( 16.67\% \)[/tex] less than Amrita's salary.
The correct answer is:
b. [tex]\( 16 \frac{2}{3} \% \)[/tex]
